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arXiv · 0804.2334

Multifractality at the quantum Hall transition: Beyond the parabolic paradigm

F. Evers·A. Mildenberger·A. D. Mirlin
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Abstract

We present an ultra-high-precision numerical study of the spectrum of multifractal exponents $Δ_q$ characterizing anomalous scaling of wave function moments $<|ψ|^{2q}>$ at the quantum Hall transition. The result reads $Δ_q = 2q(1-q)[b_0 + b_1(q-1/2)^2 + ...]$, with $b_0 = 0.1291\pm 0.0002$ and $b_1 = 0.0029\pm 0.0003$. The central finding is that the spectrum is not exactly parabolic, $b_1\ne 0$. This rules out a class of theories of Wess-Zumino-Witten type proposed recently as possible conformal field theories of the quantum Hall critical point.

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F. Evers, A. Mildenberger, A. D. Mirlin. 2008-04-15. Multifractality at the quantum Hall transition: Beyond the parabolic paradigm. https://doi.org/10.1103/physrevlett.101.116803

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